Finite Group Databasebeta

← #28372961

Subgroups — #28372961

Order 13952.

414 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16812658C211yesmaximal, characteristic, complemented
2#20295364C214yesmaximal, complemented
3#20295347C214yesmaximal, complemented
4#20295069C212yesmaximal, complemented
5#20295027C212yesmaximal, complemented
6#20294990C211yesmaximal, characteristic, complemented
7#525×C109C211yesmaximal, characteristic
8C2×#13182013C2212yes—
9#16812658—22no—
10#16812658C2214yes—
11C2×C4⋊Dic109C2212yes—
12C2×C22⋊Dic109—21no—
13C2×C4×Dic109—21no—
14#16812632C2214yescomplemented
15#16812630C2214yescomplemented
16#16812623C2214yescomplemented
17#16812620C2214yescomplemented
18C22⋊#11724784C2214yes—
19C2×#41×C109C2211yescharacteristic
20C23×C4×C109C2211yescharacteristic
21#123×C109—21no—
22C22⋊Q8×C109C2212yes—
23#121×C109C2212yes—
24#120×C109—21no—
25C4×D4×C109—22no—
26#117×C109C2211yescharacteristic
27C22×Dic109—22no—
28#13182013—24no—
29C2×#11724784C2314yes—
30C4⋊Dic109—22no—
31C4⋊Dic109C2314yes—
32C22⋊Dic109—24no—
33C4×Dic109—24no—
34C24×C109D411yescharacteristic
35#41×C109—24no—
36C2×Q8×C109C2311yescharacteristic
37C2×D4×C109—22no—
38C2×D4×C109—21no—
39C2×D4×C109C2311yescharacteristic
40C22×C4×C109—24no—
41C22×C4×C109—21no—
42C22×C4×C109D412yes—
43C22×C4×C109D411yescharacteristic
44C22×C4×C109C2312yes—
45C22×C4×C109C2311yescharacteristic
46C4⋊C4×C109—22no—
47C4⋊C4×C109C2312yes—
48C22⋊C4×C109—21no—
49C22⋊C4×C109—22no—
50C22⋊C4×C109—22no—
51C42×C109—21no—
52C23×C109—22no—
53C23×C109—21no—
54C23×C109—42no—
55C23×C109C2×D412yes—
56C23×C109C2×D411yescharacteristic
57Q8×C109—22no—
58D4×C109—22no—
59D4×C109—44no—
60D4×C109—42no—
61C2×C4×C109—22no—
62C2×C4×C109—24no—
63C2×C4×C109—24no—
64C2×C4×C109—22no—
65C2×C4×C109—21no—
66C2×C4×C109—42no—
67C2×C4×C109C2×D412yes—
68C2×C4×C109C2×D411yescharacteristic
69C2×C4×C109#4114yes—
70C2×C4×C109C2411yescharacteristic
71C2×Dic109—24no—
72C2×Dic109—44no—
73#11724784—24no—
74C22×C109—22no—
75C22×C109—22no—
76C22×C109—22no—
77C22×C109—22no—
78C22×C109—44no—
79C22×C109—41no—
80C22×C109—42no—
81C22×C109#12312yes—
82C22×C109C22×D411yescharacteristic
83C4×C109—22no—
84C4×C109—41no—
85C4×C109—42no—
86C4×C109#12312yes—
87C4×C109C2×#4112yes—
88Dic109—44no—
89C2×C109—22no—
90C2×C109—42no—
91C2×C109—81no—
92C2×C109C2×#12311yescharacteristic
93C2×C109#57512yes—
94#3093—1091nomaximal, Sylow
95C109#309311yescharacteristic, complemented, Sylow
96#525D10911yescharacteristic
97C2×#117—1091no—
98#485—1094no—
99#482—1094no—
100#428—1092no—
101#417—1092no—
102#407—1091no—
103C2×#41C2×D10911yescharacteristic
104C23×C4C2×D10911yescharacteristic
105C2×M16—1092no—
106#123—21no—
107C22⋊Q8C2×D10912yes—
108#121C2×D10912yes—
109#120—21no—
110C4×D4—22no—
111#117—1094no—
112#117—2182no—
113#117C2×D10911yescharacteristic
114C2×C4⋊C4—1092no—
115C2×C22⋊C4—2181no—
116C2×C42—2181no—
117#107—1094no—
118#106—1094no—
119#103—1094no—
120#102—1094no—
121C22⋊C8—1094no—
122C24C22⋊D10911yescharacteristic
123#41—24no—
124C2×Q8C22×D10911yescharacteristic
125C2×D4—22no—
126C2×D4—21no—
127C2×D4C22×D10911yescharacteristic
128C22×C4—24no—
129C22×C4—21no—
130C22×C4—2182no—
131C22×C4C22⋊D10911yescharacteristic
132C22×C4C22⋊D10912yes—
133C22×C4C22×D10912yes—
134C22×C4C22×D10911yescharacteristic
135M16—2184no—
136C2×C8—1094no—
137C4⋊C4—22no—
138C4⋊C4—1094no—
139C4⋊C4—2182no—
140C4⋊C4C22×D10912yes—
141C22⋊C4—21no—
142C22⋊C4—22no—
143C22⋊C4—22no—
144C22⋊C4—2184no—
145C42—21no—
146C42—2184no—
147C23—22no—
148C23—21no—
149C23—42no—
150C23C2×C22⋊D10912yes—
151C23C2×C22⋊D10911yescharacteristic
152Q8—22no—
153D4—22no—
154D4—44no—
155D4—42no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—42no—
162C2×C4—4364no—
163C2×C4—2184no—
164C2×C4C2×C22⋊D10912yes—
165C2×C4C2×C22⋊D10911yescharacteristic
166C2×C4#1318202814yes—
167C2×C4C23×D10911yescharacteristic
168C8—2184no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—22no—
173C22—44no—
174C22—41no—
175C22—42no—
176C22#1681268012yes—
177C22C22×C22⋊D10911yescharacteristic
178C4—22no—
179C4—41no—
180C4—42no—
181C4—4364no—
182C4#1681268012yes—
183C4C2×#1318202812yes—
184C2—22no—
185C2—42no—
186C2—81no—
187C2C2×#1681268011yescharacteristic
188C2#2029582412yes—
subgroupG/H
centerC22C22×C22⋊D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting, prime radical#525×C109C2
socleC22×C109C22×D4
hypercenter#525D109
hypocenterC109#3093
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#16812658C2semidirect
2. #20295364C2semidirect
3. #20295347C2semidirect
4. #20295069C2semidirect
5. #20295027C2semidirect
6. #20294990C2semidirect
14. #16812632C22semidirect
15. #16812630C22semidirect
16. #16812623C22semidirect
17. #16812620C22semidirect
95. C109#3093semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168126582
#202953642
#202953472
#202950692
#202950272
#202949902
#525×C1092
#3093109